The Performance of Some Rough Tests for Bivariate Normality Before and After Coordinate Transformations to Normality

Some rough tests for bivariate normality are employed in an attempt to quantify the intuitive notion that coordinate transformations to normality produce distributions which are “more bivariate normal” than the original variables. These tests are not rigorous procedures but are intuitively satisfying, based on natural statistics, and provide numerical measures of the “distance” of a bivariate distribution from the normal model. It is shown that, for a wide class of non-normal (X, Y) distributions, coordinate transformations to normality decrease this distance as measured by these tests. It is indicated how one may estimate the coordinate transformations and applications to correlation theory are explored.